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OverviewEverybody having even the slightest interest in analytical mechanics remembers having met there the Poisson bracket of two functions of 2n variables (pi, qi) f g ~(8f8g 8 8 ) (0.1) {f,g} = L...~[ji - [ji~ ,;=1 p, q q p, and the fundamental role it plays in that field. In modern works, this bracket is derived from a symplectic structure, and it appears as one of the main in- gredients of symplectic manifolds. In fact, it can even be taken as the defining clement of the structure (e.g., [TIl]). But, the study of some mechanical sys- tems, particularly systems with symmetry groups or constraints, may lead to more general Poisson brackets. Therefore, it was natural to define a mathematical structure where the notion of a Poisson bracket would be the primary notion of the theory, and, from this viewpoint, such a theory has been developed since the early 19708, by A. Lichnerowicz, A. Weinstein, and many other authors (see the references at the end of the book). But, it has been remarked by Weinstein [We3] that, in fact, the theory can be traced back to S. Lie himself [Lie]. Full Product DetailsAuthor: Izu VaismanPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: Softcover reprint of the original 1st ed. 1994 Volume: 118 Dimensions: Width: 15.50cm , Height: 1.10cm , Length: 23.50cm Weight: 0.343kg ISBN: 9783034896498ISBN 10: 3034896492 Pages: 206 Publication Date: 23 October 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsThe book serves well as an introduction and an overview of the subject and a long list of references helps with further study. -- Zbl. Math. The book is well done...should be an essential purchase for mathematics libraries and is likely to be a standard reference for years to come, providing an introduction to an attractive area of further research. -- Mathematical Reviews The importance and actuality of the subject, as well as the very rigorous and didactic presentation of the content, make out of this book a valuable contribution to current mathematics. The book is intended first of all to mathematicians, but it can be interesting also for a wide circle of readers, including mechanicists and physicists. -- Mathematica The book serves well as an introduction and an overview of the subject and a long list of references helps with further study. -- Zbl. Math. The book is well done...should be an essential purchase for mathematics libraries and is likely to be a standard reference for years to come, providing an introduction to an attractive area of further research. -- Mathematical Reviews The importance and actuality of the subject, as well as the very rigorous and didactic presentation of the content, make out of this book a valuable contribution to current mathematics. The book is intended first of all to mathematicians, but it can be interesting also for a wide circle of readers, including mechanicists and physicists. -- Mathematica The book serves well as an introduction and an overview of the subject and a long list of references helps with further study. -- Zbl. Math. The book is well done...should be an essential purchase for mathematics libraries and is likely to be a standard reference for years to come, providing an introduction to an attractive area of further research. -- Mathematical Reviews The importance and actuality of the subject, as well as the very rigorous and didactic presentation of the content, make out of this book a valuable contribution to current mathematics. The book is intended first of all to mathematicians, but it can be interesting also for a wide circle of readers, including mechanicists and physicists. -- Mathematica Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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